Restricted configuration path integral Monte Carlo

Abstract

Quantum Monte Carlo belongs to the most accurate simulation techniques for quantum many-particle systems. However, for fermions, these simulations are hampered by the sign problem that prohibits simulations in the regime of strong degeneracy. The situation changed with the development of configuration path integral Monte Carlo (CPIMC) by Schoof \textit{et al.} [T. Schoof \textit{et al.}, Contrib. Plasma Phys. \textbf{51}, 687 (2011)] that allowed for the first \textit{ab initio} simulations for dense quantum plasmas. CPIMC also has a sign problem that occurs when the density is lowered, i.e. in a parameter range that is complementary to traditional QMC formulated in coordinate space. Thus, CPIMC simulations for the warm dense electron gas are limited to small values of the Brueckner parameter -- the ratio of the interparticle distance to the Bohr radius -- $r_s=\bar{r}/a_B\lesssim 1$. In order to reach the regime of stronger coupling (lower density) with CPIMC, here we investigate additional restrictions on the Monte Carlo procedure. In particular, we introduce two different versions of "restricted CPIMC" where certain sign changing Monte Carlo updates are being omitted. Interestingly, one of the methods (RCPIMC) has no sign problem at all, but it is less accurate than RCPIMC+ which neglects only a smaller class of the Monte Carlo steps. Here we report extensive simulations for the ferromagnetic uniform electron gas with which we investigate the properties and accuracy of RCPIMC and RCPIMC+. Further, we establish the parameter range in the density-temperature plane where these simulations are both feasible and accurate. The conclusion is that RCPIMC and RCPIMC+ work best at temperatures in the range of $\Theta \sim 0.1\dots 0.5$ allowing to reach density parameters up to $r_s\sim 3\dots 5$, thereby partially filling a gap left open by existing \textit{ab initio} QMC methods.

References in corpus (16)

• Path Integral Monte Carlo Simulation of the Warm-Dense Homogeneous Electron Gas
• A Massive Core in Jupiter Predicted From First-Principles Simulations
• Hydrogen-Helium Mixtures in the Interiors of Giant Planets
• {\em Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas in the thermodynamic limit
• Crystallization in two-component Coulomb systems
• Ab Initio Path Integral Monte Carlo Approach to the Static and Dynamic Density Response of the Uniform Electron Gas
• Nonlinear Electronic Density Response in Warm Dense Matter
• Electron-ion scattering in dense multi-component plasmas: application to the outer crust of an accreting neutron star
• Time-dependent second Born calculations for model atoms and molecules in strong laser fields
• Fermionic path integral Monte Carlo results for the uniform electron gas at finite temperature
• Configuration Path Integral Monte Carlo Approach to the Static Density Response of the Warm Dense Electron Gas
• Restricted configuration path integral Monte Carlo
• Towards ab initio thermodynamics of the electron gas at strong degeneracy
• Finite temperature Green's function approach for excited state and thermodynamic properties of cool to warm dense matter
• Superfluidity of strongly correlated bosons in two- and three-dimensional traps
• Benchmarking vdW-DF first principle predictions against Coupled Electron-Ion Monte Carlo for high pressure liquid hydrogen

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